Solve -16x^2+98=0

$$-16 { x }^{ 2 } +98=0$$

Solve for x

$$x = \frac{7 \sqrt{2}}{4} \approx 2.474873734$$

$$x = -\frac{7 \sqrt{2}}{4} \approx -2.474873734$$

Steps by Finding Square Root

Subtract 98 from both sides. Anything subtracted from zero gives its negation.

$$-16x^{2}=-98$$

Divide both sides by -16.

$$x^{2}=\frac{-98}{-16}$$

Reduce the fraction \frac{-98}{-16} to lowest terms by extracting and canceling out -2.

$$x^{2}=\frac{49}{8}$$

Take the square root of both sides of the equation.

$$x=\frac{7\sqrt{2}}{4} x=-\frac{7\sqrt{2}}{4}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-16x^{2}+98=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -16 for a, 0 for b, and 98 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)\times 98}}{2\left(-16\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)\times 98}}{2\left(-16\right)}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64\times 98}}{2\left(-16\right)}$$

Multiply 64 times 98.

$$x=\frac{0±\sqrt{6272}}{2\left(-16\right)}$$

Take the square root of 6272.

$$x=\frac{0±56\sqrt{2}}{2\left(-16\right)}$$

Multiply 2 times -16.

$$x=\frac{0±56\sqrt{2}}{-32}$$

Now solve the equation x=\frac{0±56\sqrt{2}}{-32} when ± is plus.

$$x=-\frac{7\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±56\sqrt{2}}{-32} when ± is minus.

$$x=\frac{7\sqrt{2}}{4}$$

The equation is now solved.

$$x=-\frac{7\sqrt{2}}{4} x=\frac{7\sqrt{2}}{4}$$